The present invention relates to a Laplace transform impedance spectrometer and its measurement method. More particularly, the method of and apparatus for measuring Laplace transform impedance can provide a high quality of wide-ranged impedance spectrum measurement within a minimal time with, applicable to the various electrical circuits, non-linear devices, capacitors, and other electrochemical devices such as primary and secondary batteries and fuel cells.
The technique of measuring impedance spectrum of the electrical or electrochemical device can be widely applied to a characterization of an electrical circuit, material evaluation, corrosion protection, evaluation of properties, quality control and capacity estimation of batteries.
As a widely used measurement for impedance spectrum, there is a method of applying a periodic perturbation signal at a certain frequency, and measuring the amplitude and phase of the response, for example, by using frequency response analyzer.
U.S. Pat. Nos. 4,196,475 and 3,634,760 introduce a method of analyzing a response characteristic at a single frequency. But the method stated in the above patent applications has problems that it must use expensive devices such as a signal generator and phase detector, and it needs at least two periods of signal to remove transient effects. In addition, it takes a long time to proceed the successive measurements for each frequency when a spectrum at a plurality of frequencies is required.
When using the Fast-Fourier Transform (hereinafter, it is referred to FFT) in which a response signal is fast-Fourier transformed by means of an excitation signal of the multiple-superposed sine waves (refer to G. S. Popkirov and R. N. Schindler, Rev. Sci. Instrum. 63, 5336 (1992)), the phase detector is not required and the time required for the spectrum measurement with respect to the plurality of frequencies is relatively short in contrast to the method of using the frequency response analyzer.
Furthermore, the FFT method examines the linearity of the system for testing by comparing input and output power spectrums and thus provides a high quality of impedance spectra. The FFT method, however, takes more than double the measurement time corresponding to the period of the minimum frequency in the measurement frequency range and, besides, requires a complicated signal generator and a large capacity of memory device.
Since the applied perturbation signal is generated by superposition of non-overlapping frequencies, the impedance spectrum is obtained at odd times of the minimum frequency. Therefore, only a few number of impedance data points can be obtained at low frequency region.
U.S. Pat. No. 5,633,801 describes a method of using current pulse instead of a plurality of superposed sine waves in impedance measurement. In this method, however, considerable frequency dependent noise due to a frequency aliasing and transient effect sometimes cause a measurement error, thus having a problem in a reliability of the measurement results and confidence interval (W. J. Thomson and J. R. Macdonald, Proc. Natl. Acad. Sci. USA, 90, 6904 (1993)).
A method stated in U.S. Pat. No. 5,794,008, which uses a discrete Laplace transform in analyzing the pulse signal in order to get a high quality of measurement result at a frequency region, requires a long operation time and a large memory size.
The above method needs, in analysis, computation at each measurement data point, and the number of the measurement data points is determined as double of the ratio of the maximum and minimum frequencies so that in case of eight decades of measurement sections, one million times of computation process is required for one megabyte memory.
Integration step required for transformation sometimes gives oscillating results.
It is also difficult to determine the accuracy of the measurement using this method, as in the pulse FFT, and if the system for testing is non-linear, it is possible to get the impedance spectrum from the measurement but there is no physical meaning on it.
Accordingly, an object of the present invention is to provide a carrier function Laplace transform impedance spectrometer and its measurement method, obtaining a high quality of wide-ranged impedance spectrum within a minimal time for characterization of the various electrical circuits, non-linear devices, capacitors, and other electrochemical devices such as primary, secondary batteries and fuel cells.
To accomplish an object of the present invention, a Laplace transform impedance spectrometer, includes:
a galvanostat/potentiostat for applying constant voltage, constant current or constant load to the electrochemical device by employing constant voltage source, constant current source or constant load element such as a resistor and thereby detecting voltage and current of the electrochemical device resulting from above excitation;
a voltage/current output unit for removing noise out of voltage and current detected in the galvanostat/potentiostat, also removing bias voltage and current and outputting signals;
a two channel analog/digital converter for converting the voltage and current output from the voltage/current output unit into digital signal; and
a control means for fitting the digital voltage and current output from the analog/digital converter to Laplace transform carrier function to thereby generate impedance spectrum and storing its data.
To accomplish the other object of the invention, a method of measuring Laplace transform impedance, includes the steps of:
(1) detecting a response signal of an object whose impedance will be measured;
(2) obtaining parameters of a carrier function by linearly or non-linearly fitting the response signal in step (1) to the carrier function which has an analytical Laplace transform;
(3) calculating an impedance function in the frequency domain by using an analytic relation between the carrier function in time domain and its Laplace transform function, using parameters of the carrier function obtained through the fitting results in step (2);
(4) calculating the impedance spectrum in a frequency range determined by measurement interval and sampling rate by using impedance function calculated in step (3), and calculating the measurement error of the frequency domain impedance spectrum out of the standard deviation of the parameters and its correlation; and
(5) displaying the frequency domain impedance spectrum calculated in step (4) in a fixed form and storing the result.
Specifically, the invention provides a Laplace transform spectrometer providing high measurement accuracy, speed and a simple architecture.
The invention relates to a method of obtaining impedance spectra by using Laplace transform carrier functions suitable for transient response of step signals. In a measurement, the spectrometer requires just a small size memory for computation and requires only linear operations on measured data which do not include integration. And, it is different from other art in that it allows use of a standard statistic means for assigning confidence interval to a frequency domain measurement data, providing therefore analysis of the quality of the measurement and the linearity of the system for testing.